A time-domain formulation of flexural vibrations in damped rectangular
orthotropic plates has been developed, in order to investigate transient and
nonlinear excitation of plates. The model includes three basic mechanisms of
damping: thermoelasticity, viscoelasticity, and radiation. As a consequence, the
four rigidity factors are modified by perturbation terms, each perturbation term
corresponding to one specific damping mechanism. The thermoelastic term is
derived from the coupling between the thermoelastic stress-strain relationships
and the heat diffusion equation. The second perturbation term is obtained from
the standard generalized partial differential equation formulation of
viscoelasticity. The third term is obtained through a Pade approximant of the
damping factor which governs the radiation of an infinite plate coupled with a
light fluid. The flexural equations are solved numerically in the particular
case of a sphere impacting the plate with the help of a finite difference scheme
of second order in time and fourth order in space. A simulated sound pressure is
then obtained by a simple discrete form of the Rayleigh integral. The simulated
tones show the relative relevance of the three damping mechanisms, for four
different materials: aluminium, glass, carbon fibers, and wood.